Nuprl Lemma : bpa-norm_wf
∀p:ℕ+. ∀x:basic-padic(p).  (bpa-norm(p;x) ∈ basic-padic(p))
Proof
Definitions occuring in Statement : 
bpa-norm: bpa-norm(p;x)
, 
basic-padic: basic-padic(p)
, 
nat_plus: ℕ+
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
basic-padic: basic-padic(p)
, 
bpa-norm: bpa-norm(p;x)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
nat: ℕ
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
ifthenelse: if b then t else f fi 
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
prop: ℙ
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
ge: i ≥ j 
, 
int_upper: {i...}
, 
p-adics: p-adics(p)
, 
nat_plus: ℕ+
, 
decidable: Dec(P)
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
subtype_rel: A ⊆r B
, 
top: Top
, 
true: True
, 
int_seg: {i..j-}
, 
nequal: a ≠ b ∈ T 
, 
lelt: i ≤ j < k
, 
p-units: p-units(p)
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
Lemmas referenced : 
eq_int_wf, 
bool_wf, 
eqtt_to_assert, 
assert_of_eq_int, 
false_wf, 
le_wf, 
eqff_to_assert, 
equal_wf, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
neg_assert_of_eq_int, 
upper_subtype_nat, 
nat_properties, 
nequal-le-implies, 
zero-add, 
decidable__lt, 
not-lt-2, 
add_functionality_wrt_le, 
add-commutes, 
le-add-cancel, 
less_than_wf, 
int_seg_wf, 
exp_wf2, 
p-shift_wf, 
p-unitize_wf, 
not-equal-2, 
p-units_wf, 
p-adics_wf, 
p-mul_wf, 
p-int_wf, 
subtract_wf, 
int_seg_properties, 
int_upper_properties, 
nat_plus_properties, 
decidable__le, 
full-omega-unsat, 
intformand_wf, 
intformnot_wf, 
intformle_wf, 
itermConstant_wf, 
itermSubtract_wf, 
itermVar_wf, 
intformless_wf, 
itermAdd_wf, 
int_formula_prop_and_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_subtract_lemma, 
int_term_value_var_lemma, 
int_formula_prop_less_lemma, 
int_term_value_add_lemma, 
int_formula_prop_wf, 
basic-padic_wf, 
nat_plus_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
sqequalHypSubstitution, 
productElimination, 
thin, 
sqequalRule, 
cut, 
introduction, 
extract_by_obid, 
isectElimination, 
setElimination, 
rename, 
because_Cache, 
hypothesis, 
natural_numberEquality, 
unionElimination, 
equalityElimination, 
independent_isectElimination, 
independent_pairEquality, 
dependent_set_memberEquality, 
equalityTransitivity, 
equalitySymmetry, 
independent_pairFormation, 
hypothesisEquality, 
dependent_pairFormation, 
promote_hyp, 
dependent_functionElimination, 
instantiate, 
cumulativity, 
independent_functionElimination, 
voidElimination, 
hypothesis_subsumption, 
applyEquality, 
lambdaEquality, 
isect_memberEquality, 
voidEquality, 
intEquality, 
productEquality, 
addEquality, 
setEquality, 
approximateComputation, 
int_eqEquality
Latex:
\mforall{}p:\mBbbN{}\msupplus{}.  \mforall{}x:basic-padic(p).    (bpa-norm(p;x)  \mmember{}  basic-padic(p))
Date html generated:
2018_05_21-PM-03_25_13
Last ObjectModification:
2018_05_19-AM-08_22_41
Theory : rings_1
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